To understand how single lipid bilayers might form in cells, we have examined the equilibrium phase diagram of dilute dimyristoylphosphatidylglycerol (DMPG) dispersions in water. Using surface pressure measurements, quasielastic light scattering and phase-contrast microscopy, unilamellar vesicle formation has been observed at a critical temperature, T*, the identical temperature where single bilayers form in films of the lipid at the air-water surface. T* is ca. 8°C higher than the gel-liquid-crystal transition temperature, T,, for DMPG dispersions. At T < T*, DMPG exists as a jelly which appears to consist of a matrix of extended bilayer sheets.At T > T*, DMPG dispersions form rnultilamellar vesicles. The solubility of DMPG in water, X,, was measured over the temperature interval of 8-40 "C. The function dlnX,/dT was found to be discontinuous at T, , but was continuous in the temperature interval that encompasses T*.

Methods for expressing, measuring, and correlating drop‐size distribution data for centrifugal spray nozzles are discussed. A method for collecting spray droplets in liquid nitrogen is described which is rapid and efficient for most sprayed liquids which freeze above —20°C. Comprehensive correlations for drop‐size distributions are reported based on 114 runs performed with the liquid nitogen method.

CP H hs 1 L m P S t T z = heat capacity at constant pressure, L2/t2T = generalized local transport coefficient, L3/T = inverse of surface resistance, L / t = thickness of stagnant film; average thickness of = thickness of liquid layer in wetted wall column, L = number of capacitances or capacitors in multiple = potential, pc, T in M/Lt2 or C in M/L3 = frequency or fractional rate of surface renewal, = time of process on the macroscopic scale, t = temperature, T = distance from interfacial plan, L fluid elements, L capacitances model, dimensionless t-' Greek Letters y = hS/K, L-' 6 = impulse function, t-1 0 = contact time or age, t K = generalized molecular diffusivity, Lz/t 1~ = 3.14159 . . ., dimensionless p = density of fluid or particles, M / L 3 7 = mean residence time, t 4 = contact time (or age) disMbution function, t-1 Jli = instantaneous local transport rate, ML2/t3 or M / t Jl = average local transfer rate, ML2/C? or M / t = average transfer rate for any time interval, ML2/t" or M / t Subscripts b 1 = quantity evaluated at bulk stream = infinite thickness of fluid elements 0 y = no surface resistance 00 = infinitely many capacitors LITERATURE CITED = quantity evaluated at interface 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.14. 15.Although much attention has been given recently to the development of methods for the determination of the optimal control of a batch reactor or the best operating conditions for a tubular reactor, a number of difficulties and uncertainties still remain, especially when the analysis involves an exothermic reversible reaction. Several investigators (1, 5, 8 ) have been concerned with the establishment of the optimum temperature profile along a tubular reactor, from which the optimal control (heat removal rate) must then be obtained. Others (2, 10 to 12) Daniel Y. C. KO is with Gulf Research and Development Conipany,have studied methods suitable for direct determination of the heat flux profile, some of which resulted in the possible appearance of singular control for a portion of the reactor length. The present authors have looked further into the occurrence of such singular problems during the applicatjop pf tbq theory of optimal control and have developed an improved approach to the determination of the optimal heat transfer coefficient distribution along a tubular reactor (6, 7 ) . This paper presents the details of an application of the method of solution presented in the companion paper (7)to the optimal design of a tubular reactor. It is shown that, in general, if the reactor is "sufficiently long," the optimal

Based on the data reported by Rossini e t al. (9) analytical expressions have been developed for the calculation of enthalpies at zero pressure as functions of temperature for normal paraffins ranging from methane through octane. The coefficients of these equations have been found to correlate linearly with molecular weight, thus allowing the enthalpy relationships for hydrocarbons heavier than octane to be determined by extrapolation. The enthalpy of mixtures at zero pressure can then be obtained by combining the enthalpies of the individual components on an additive basis, weighted by the mole fractions.Corrections due to nonideal gaseous behavior have been developed in equation form from the work of Lydersen, Greenkorn, and Hougen (7) in terms of the reduced temperature TR and the critical compressibility factor zo of the substance. These corrections have been developed for both the saturated vapor and saturated liquid states and can be applied to the determination of the enthalpy of mixtures at these conditions. The results of this method have been compared with the experimental enthalpy data available for in excellent ogreement.

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